<p>
    Implement a program that performs the leaky ReLU activation function on a vector of floating-point numbers. The leaky ReLU function is defined as:
    \[ f(x) = \begin{cases} 
      x & \text{if } x > 0 \\
      \alpha x & \text{if } x \leq 0
    \end{cases} \]
    where \(\alpha\) is a small positive constant (0.01 in this problem).
  </p>
  
  <h2>Implementation Requirements</h2>
  <ul>
    <li>External libraries are not permitted</li>
    <li>The <code>solve</code> function signature must remain unchanged</li>
    <li>The final result must be stored in vector <code>output</code></li>
    <li>Use \(\alpha = 0.01\) as the leaky coefficient</li>
  </ul>
  
  <h2>Example 1:</h2>
  <pre>
  Input:  x = [1.0, -2.0, 3.0, -4.0]
  Output: y = [1.0, -0.02, 3.0, -0.04]</pre>
  
  <h2>Example 2:</h2>
  <pre>
  Input:  x = [-1.5, 0.0, 2.5, -3.0]
  Output: y = [-0.015, 0.0, 2.5, -0.03]</pre>
  
  <h2>Constraints</h2>
  <ul>
    <li>1 ≤ <code>N</code> ≤ 100,000,000</li>
    <li>-1000.0 ≤ <code>input[i]</code> ≤ 1000.0</li>
  </ul> 